Translate to an equation and solve the following: The difference of p and one-sixth is two-thirds.

Answer:

1) The line AB can be renamed as BA   and  h

2 ) Points B, D and C are on the same line.

3)  ABE is the another name given to the plane F.

4) E is another point which is not coplanar with ABC.

5) Another name for CD is g or DC

6) AB CB DB are rays with end points B

7) BC and BD are opposite rays .

8) CB or g is another name for CD

Step-by-step explanation:

1) The line AB can be renamed as BA   and h

2 ) Collinear points are those points which lie on the same line. So points B, D and C are on the same line.

3) Points ABE define the plane F so ABE is the another name given to the plane F.

4) E is another point which is not coplanar with ABC. ( Coplanar points are those points which are situated on the same plane)So from the picture we see that point E lies far away from the plane of ABC.

5) Another name for CD is g or DC

6) AB CB DB are rays with end points B

7) BC and BD are opposite rays . ( A ray is a line which extends indefinitely . In simple words it has no end point. It may pass through certain points. It is represented by an arrow at one end.)

8) CB or g is another name for CD

Answer:

16:12

Step-by-step explanation:

if there is 12 boys, that leaves the other 16 to be girls

Answer:

4:3

Step-by-step explanation:

If there are 12 boys then 28-12=16

So there are 16 girls

The girls to boys ratio is 16:12 and you simplify

Now it's 4:3

1.

[tex]f(x)=-3x\qquad g(x)=5x-6\\\\g(f(x))=5(-3x)-6=\boxed{-15x-6}[/tex]

2.

[tex]f(x)=x-6\qquad g(x)=x^2+6x-2\\\\g(f(x))=(x-6)^2+6(x-6)-2=x^2-12x+36+6x-36-2=\\\\=\boxed{x^2-6x-2}[/tex]

3.

[tex]f(x)=4x+3\qquad g(x)=2x^2-x+1\\\\g(f(x))=2(4x+3)^2-(4x+3)+1=2(16x^2+24x+9)-4x-3+1=\\\\=32x^2+48x+18-4x-3+1=\boxed{32x^2+44x+16}[/tex]

4.

[tex]f(x)=2x^2\qquad g(x)=8x^2+3x\\\\g(f(x))=8(2x^2)^2+3(2x^2)=8\cdot4x^4+6x^2=\boxed{32x^4+6x^2}[/tex]

Answer:

Choice C. [tex]3,\! 780[/tex].

Step-by-step explanation:

The word "[tex]\verb!TENNESSEE![/tex]" contains nine letters:

If all these nine letters are unique, the number of possible arrangements would be:

[tex]P(9, 9) = 9! = 362,\! 880[/tex].

However, because some of these letters were not unique, a large number of that [tex]362,\!880[/tex] arrangements would be duplicates. What would be the exact number of duplicates? Start by considering giving each of the duplicate letters an index number. For example, consider the duplicates due to the letter "[tex]\verb!E![/tex]". There are four [tex]\verb!E![/tex]'s in [tex]\verb!TENNESSEE![/tex]. Label them as [tex]\verb!E!_1[/tex], [tex]\verb!E!_2[/tex], [tex]\verb!E!_3[/tex], and [tex]\verb!E!_4[/tex]:

[tex]\begin{array}{ccccccccc}\verb!T! & \verb!E! & \verb!N! & \verb!N! & \verb!E! & \verb!S! & \verb!S! & \verb!E! & \verb!E! \\ & \uparrow & & & \uparrow & & & \uparrow & \uparrow \\ & \verb!E!_1 & & & \verb!E!_2 & & & \verb!E!_3 & \verb!E!_4\end{array}[/tex].

These four [tex]\verb!E![/tex] can be shuffled and rearranged to give a large number of duplicates:

[tex]\begin{array}{r|ccccccccc}& \verb!T! & \verb!E! & \verb!N! & \verb!N! & \verb!E! & \verb!S! & \verb!S! & \verb!E! & \verb!E! \\ &&\uparrow&&&\uparrow&&&\uparrow &\uparrow\\ 1 & & \verb!E!_1 & & & \verb!E!_2 & & & \verb!E!_3 & \verb!E!_4\\ 2 & & \verb!E!_1 & & & \verb!E!_2 & & & \verb!E!_4 & \verb!E!_3 \\ 3 & & \verb!E!_1 & & & \verb!E!_4 & & & \verb!E!_3 & \verb!E!_2 \\\ \vdots & & \vdots & & & \vdots & & & \vdots&\vdots \\4! = 24&&\verb!E!_4 & & & \verb!E!_3 & & & \verb!E!_2 & \verb!E!_1 \end{array}[/tex].

Each of these duplicate corresponds to a unique way for arranging four unique item in a row. There are [tex]4! = 24[/tex] ways to arrange four unique items in a row. Therefore, for each arrangement that is truly unique, the letter "[tex]\verb!E![/tex]" alone would have caused the arrangement to be counted [tex]4! = 24[/tex] times if the nine letters were assumed to be unique.

At the same time, letters "[tex]\verb!N![/tex]" and "[tex]\verb!S![/tex]" would further exaggerate the count by a factor of [tex]2[/tex] each. On the other hand, the letter [tex]\verb!T![/tex] appeared only once and would not create duplicates.

Overall, if the nine letters were assumed to be unique, each arrangement that is truly unique would have been counted:

[tex]4! \times 2! \times 2! \times 1! = 96\; \text{times}[/tex].

The count based on the incorrect assumption (that the nine letters are all distinct) is [tex]362,\!880[/tex]. Divide that count by the factor of exaggeration ([tex]4! \times 2! \times 2! \times 1! = 96[/tex]) to find the number of arrangements that are truly unique:

[tex]\begin{aligned} & 362,\!880 \times \frac{1}{4! \times 2! \times 2! \times 1!} = 3,\!780\end{aligned}[/tex].

4 is equivalent to the given expression.

It is required to find the equivalent to the given expression.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined.

Given:

The given expression is

(3−2^2)+5

=(3-4)+5

=(-1)+5

=4

Therefore, 4 is equivalent to the given expression.

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Answer:

g = 2

Step-by-step explanation:

5(2-g) = 0

10 - 5g = 0

-5g = -10

g = -10/-5

  = 2

Answer:

The simple interest was found to be $9.6 after 1 year at 3%

Step-by-step explanation:

Given that

principal p= $350

rate r= 3%= 3/100= 0.03

time t= 1 year

The expression for the simple interest is given as

SI= p*r*t

SI= 320*0.03*1

SI= $9.6

After 1 year at 3% the simple interest is $9.6

Simply put the extra money earned after an investment is called the simple interest

Answer:

Here is your answer-

x³×x⁷

you just need to add the powers here.

x¹⁰

Answer:

Fathom in reference to what does this line interpret?

Answer:

d.)

C = 1200x + 765

Step-by-step explanation:

The substitution property of equality allows you to substitute an expression for a variable. Since y equals 40x + 25, you can substitute (40x + 25) for y in the C = 30y + 15 equation:

C = 30y+ 15

y = 40x + 25

C = 30y + 15

C = 30(40x + 25) + 15

C = 1200x + 750 + 15

C = 1200x + 765

The equivalent expression for C = 1200x+765.

C = 30y+15; y = 40x+25 Equivalent relation between C and x to determine.

Equations are defined as the mathematical expression intended meaning to something that contains an equal sign.

Here, C=30y+15
        y = 40x+25
Putting y in C = 30y+15
          C= 30(40x+25)+15
          C = 1200x + 750 +15
          C = 1200x +765

Thus, the equivalent expression for C = 1200x+765.  

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Answer: 5/6

Step-by-step explanation:

Answer:

a and c are undefined.

b and d are zero.

Step-by-step explanation:

Vertical lines are undefined because of division by 0  (a and c).

The run is zero.

Horizontal lines have a slope of 0 (b and d).

The rise is zero.

Answer:

55-7=48

48÷-6=-8

y=-8

......

Answer:

-8 = y

Step-by-step explanation:

55=7-6y

Subtract 7 from each side

55-7=7-6y-7

48 = -6y

Divide each side by -6

48/-6 = -6y/-6

-8 = y

Answer:

My answer to the question is 34.0

Answer:

|x - 89| ≤ 5  

Step-by-step explanation:

Here the range is 84 to 94 ft, with the midpoint being 89 and the greatest variation from the midpoint being ±5.  

We adapt |x| ≤ a as follows:  replace x with 'x - 89' and a with 5:

|x - 89| ≤ 5  

It is customary to regard '89' as the 'center' of the solution interval and 5 as the 'maximum difference' or 'radius' separating x from this center.

Answer:

(a) The probability that the house size is over 1371 square feet is 0.4483.

(b) The probability that the house size is under 1296 square feet is 0.3974.

(c) The probability that the house size is between 773 and 1637 square feet is 0.9344.

Step-by-step explanation:

We are given that the sizes of houses in Kenton County are normally distributed with a mean of 1346  square feet with a standard deviation of 191 square feet.

Let X = the sizes of houses in Kenton County

The z-score probability distribution for the normal distribution is given by;

                               Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean size of houses = 1346 square feet

            [tex]\sigma[/tex] = standard deviation = 191 square feet

(a) The probability that the house size is over 1371 square feet is given by = P(X > 1371 square feet)

        P(X > 1371) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{1371-1346}{191}[/tex] ) = P(Z > 0.13) = 1 - P(Z [tex]\leq[/tex] 0.13)

                                                             = 1 - 0.5517 = 0.4483

The above probability is calculated by looking at the value of x = 0.13 in the z table which has an area of 0.5517.

(b) The probability that the house size is under 1296 square feet is given by = P(X < 1296 square feet)

        P(X < 1296) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{1296-1346}{191}[/tex] ) = P(Z < -0.26) = 1 - P(Z [tex]\leq[/tex] 0.26)

                                                             = 1 - 0.6026 = 0.3974

The above probability is calculated by looking at the value of x = 0.26 in the z table which has an area of 0.6026.

(c) The probability that the house size is between 773 and 1637 square feet is given by = P(773 square feet < X < 1637 square feet)

       P(773 < X < 1637) = P(X < 1637) - P(X [tex]\leq[/tex] 773)

      P(X < 1637) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{1637-1346}{191}[/tex] ) = P(Z < 1.52) = 0.9357

       P(X [tex]\leq[/tex] 773) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{773-1346}{191}[/tex] ) = P(Z [tex]\leq[/tex] -3) = 1 - P(Z [tex]\leq[/tex] 3)

                                                             = 1 - 0.9987 = 0.0013

The above probabilities are calculated by looking at the value of x = 1.52 and x = 3 in the z table which has an area of 0.9357 and 0.9987 respectively.

Therefore, P(773 square feet < X < 1637 square feet)  = 0.9357 - 0.0013 = 0.9344.  

Answer:

The answer is z=-35.

5=z/-4-3.=-35.

And if the question is the other way around that the -3 is for the whole question and not with the -4 like if they are not together then the answer is -32.

Answer:

three consecutive integers that add up to 675 are 224, 225, and 226.

Step-by-step explanation:

Answer:

x=7, y=-2 (negative 2)

Step-by-step explanation:

Answer:

[tex]4p\geq 12[/tex]

Step-by-step explanation:

So, when there were 4 innings left, the score was 17 to 6 and Kim was losing.

Since the score was 17 to 6, in order for her to win, they must've scored at least another 12 points.

This is because we are told that the other team didn't score, so their final score is 17.

And for Kim to win, they must have more points, so their must've scored at least 12 points for their score to be 18.

And we also know that they scored the same per inning for the next four innings.

Thus, in an inequality, this is:

[tex]4p\geq 12[/tex]

The score per inning times 4 innings must be greater than or equal to 12:

Further notes:

To solve, divide both sides by 4:

[tex]p\geq 3[/tex]

In other words, Kim's team must've scored at least 3 points per inning.

Also note that this solution include only integers, since you can't score 3.5 points.

Answer:

Tom's pay for the week should be over 500 dollars. Sorry if this isn't very helpful. :(

Step-by-step explanation:

Answer:

D. [tex]5\cdot\frac{1}{2}[/tex]

Step-by-step explanation:

[tex]5\div 2 =\frac{5}{2} \\\\5\times\frac{1}{2}\\\\=\frac{5}{1}\times\frac{1}{2}\\\\=\frac{5}{2} \\[/tex]

Answer:

Output 2019 = 1.425 million dollar

Step-by-step explanation:

Given:

Output 2009 = 1.5 million dollar

Projected decrease output = 5%

Find:

Output 2019

Computation:

Output 2019 = Output 2009[100% - Projected decrease output]

Output 2019 = 1.5 [100% - 5%]

Output 2019 = 1.425 million dollar

Answer:

$ 2250

Step-by-step explanation:

3375 = s³

s = ∛3375

s = 15 ft.

floor area = s² = (15 * 15)

floor area = 225 ft²

the contractor charges $10 per ft².

therefore,  

the hardwood cost = 225  x  $10 = $2250

Answer:

$2,250.

Step-by-step explanation:

So first, we need to find the area of the floor (the side shaded green). To do so, we first need to find the length of the one side of the room.

Since we know that the room is a cube, all side lengths are equivalent. And since we are given that the volume of the room is 3375, we can find the length of the side.

The volume of a cube is given by the formula:

[tex]V=s^3[/tex]

Substitute 3375 for V:

[tex]s^3=3375[/tex]

Take the cube root of both sides:

[tex]s=\sqrt[3]{3375}=15[/tex]

So, the side length of the room is 15.

This means that the area of the floor is:

[tex]A=(15)^2\\A=225\text{ in}^2[/tex]

They charge $10 per square foot. There are 225 square feet. Thus, the total cost will be:

[tex]10(225)=$2250[/tex]

$2,250.

Answer: [tex]-6[/tex]

Do Keep Change Flip (KCF)

Keep: [tex]15/4[/tex]

Change: ÷ into ×

Flip: [tex]-5/8[/tex] into [tex]8/-5[/tex]

Multiply

[tex]15/4*8/-5=120/-20[/tex]

Divide

[tex]120/-20=-6[/tex]

Answer: -6

Step-by-step explanation: Factor your numerator and your denominator, then cancel you common factors.

I hope this helps you out! ♥

Answer:

1/4

Step-by-step explanation:

Since the denominatior is the same, we can look at only the numerator. So 7/8 - 5/8 is basically 7 - 5 which is 2.

The denominator doesn't change so it's 2/8. We can further simplify this into 1/4.

Answer:

The radius is 8 inches

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

Assuming you mean 320 pi for the volume

320  pi = pi r^2 ( 5)

320 =5pi r^2

Divide each side by 5pi

320 pi / 5pi = 5 pi r^2 / 5pi

64 = r^2

Take the square root of each side

sqrt(64) = sqrt(r^2)

8 = r

The radius is 8 inches

Answer:

[tex]\Huge \boxed{\mathrm{4.51 \ inches}}[/tex]

[tex]\rule[225]{225}{3}[/tex]

Step-by-step explanation:

[tex]V=\pi r^2 h[/tex]

The volume is 320 in³.

The height is 5 in.

[tex]320=\pi r^2 * (5)[/tex]

Solving for [tex]r[/tex].

Dividing both sides by 5.

[tex]64=\pi r^2[/tex]

Dividing both sides by [tex]\pi[/tex].

[tex]20.371833=r^2[/tex]

Taking the square root of both sides.

[tex]r= 4.513517[/tex]

The radius is 4.51 inches.

[tex]\rule[225]{225}{3}[/tex]

Answer: is D

Answer is D

Using the simple method of quadratic expression:

we find two  numbers(the first and last word) that when we multiply is the same as when we add them together.

a²+9a+20

a²+4a+5a+20

The answer is D

a(a+4)+5(a+4)

(a+4)(a+5)

Answer:

Quantity of ice cream  = 50 litre

Quantity of ice cream contained in one ice cream tub = 750 ml

1 litre = 1000 mL

Quantity of one ice cream tub in litres = 0.75 litres

we need to calculate the number of ice cream tubs filled by using 50 litres of ice cream

Number of ice cream tubs filled = 66 tubs 500 ml

hope it helps :)

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